Abstract
Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction \(P\subset SO(M)\) of the structure group \(SO(\dim M)\) to a subgroup G. We say that a G-structure M is minimal if P is a minimal submanifold of SO(M), where we equip SO(M) in the natural Riemannian metric. We give non-trivial examples of minimal G-structures for \(G=U(\dim M/2)\) and \(G=U((\dim M-1)/2)\times 1\) having some special features—locally conformally Kähler and \(\alpha \)-Kenmotsu manifolds, respectively.
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I wish to thank anonymous referee for many suggestions that led to improvement of the paper.
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Niedziałomski, K. Examples of Minimal \(\varvec{G}\)-structures. Results Math 73, 63 (2018). https://doi.org/10.1007/s00025-018-0824-7
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DOI: https://doi.org/10.1007/s00025-018-0824-7
Keywords
- G-structure
- intrinsic torsion
- minimal submanifold
- locally conformally Kähler manifold
- \(\alpha \)-Kenmotsu manifold